2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62662In this paper, we give a new simplified calculation of the Lusternik-Schnirelmann category of closed 3-manifolds. We also describe when 3-manifolds have detecting elements and prove that 3-manifolds satisfy the equality of the Ganea conjecture.Latex, 10 pagesAlgebraic Topologytext